Real-Life Math Challenge

Curriculum Area and Level

Aligned with Common Core State Standards (CCSS):
Grade 8 – The Number System & Expressions, Equations, and Inequalities

• CCSS.MATH.CONTENT.8.EE.C.7: Solve linear equations in one variable.
• CCSS.MATH.CONTENT.8.NS.A.1: Know that there are numbers that are not rational, and approximate them by rational numbers.
• CCSS.MATH.CONTENT.8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph.

---

Learning Objective:

By the end of the lesson, students will apply their understanding of linear equations and proportional relationships to solve a real-world problem through a hands-on, group-based math challenge.

---

Materials Needed:

• Whiteboard and markers
• Individual dry-erase boards and markers for each group
• Printed challenge cards (created prior to class)
• Rulers
• Scratch paper
• Graph paper
• Multi-colored sticky notes
• A bowl of small prizes (e.g., erasers or fun stickers)

---

Lesson Outline (45 Minutes)

---

1. Warm-Up (5 Minutes)

Focus: Build excitement and recall prior learning

• Write the phrase “Math in Action!” on the whiteboard.
• Briefly recap concepts of linear equations and proportional reasoning in 2 minutes. For example:
  • “What do we know about slope?”
  • “What does ‘y = mx + b’ represent?”
• Pose a warm-up challenge:
  “If a phone plan charges $20 per month and an additional $10 per GB of data, how much would you pay for 3 GB?”
  • Allow students to solve individually on personal dry-erase boards (2 minutes).
  • Quickly review the correct solution with the class (1 minute).

---

2. Introduction to the Math Challenge (5 Minutes)

Focus: Explain the activity and excite students

1. Hook:

   • Say: “Imagine you’ve just been hired as a financial planner for a small movie production. They need YOUR math skills to solve a tricky problem!”
   • Divide the class into 5 teams of 5 students each.

2. Set the Task:
   Provide brief instructions for the Real-Life Math Challenge:

   • Teams will solve a challenging scenario using their math skills.
   • They will graph relationships, estimate costs, and balance equations.
   • Teams that complete all parts correctly will win a prize.

3. Distribute challenge cards (one per group), rulers, graph paper, and sticky notes.

---

3. Main Math Challenge (30 Minutes)

Focus: Team-based problem solving with differentiated tasks

Challenge: Movie Set Water Usage

Scenario:

• You are managing a water supply for a movie set. The production uses:
  • 50 gallons/day for general operations.
  • 8 gallons/day per actor (there are 15 actors).
  • Bonus question: A local supplier is offering an alternative plan where water costs $1.50 per gallon for the first 200 gallons, and $2.00 per gallon after that. Which plan is cheaper for a 7-day shoot?

---

Phase 1 (5 Minutes): Understanding the Problem

• Teams analyze the problem and underline key numbers on their challenge card.
• They use sticky notes to create a list of the required calculations.

---

Phase 2 (15 Minutes): Solving the Problem

Team Roles: Assign roles to encourage collaboration:

• Lead Solver: Sets up equations and guides calculations
• Recorder: Writes down calculations and results
• Graph Maker: Draws and labels graphs of water usage
• Checker: Double-checks all calculations
• Presenter: Prepares the summary for class discussion

Teams work to:

1. Create an equation that models the water usage per day.
   • Example: y = 8(15) + 50
2. Graph the daily water usage for 7 days.
3. Calculate the total water cost for the original plan.
4. Solve the bonus question by comparing water costs.

---

Phase 3 (5 Minutes): Preparing a Presentation

• Teams create a 2-minute explanation of their solutions, focusing on the math used and their reasoning.

---

4. Class Discussion and Closure (5 Minutes)

Focus: Share learning and reflect

1. Presentations (3 Minutes):
   Each team presents their solution to the class. Use guiding questions:

   • “How did your graph help you solve the problem?”
   • “What strategies did your team use to check your work?”

2. Debrief (2 Minutes):

   • Praise teamwork and effort.
   • Reflect on how math applies to everyday challenges:
     “Why is it important to understand proportional relationships and equations in real-world contexts?”

---

Differentiation Strategies:

• Below Level: Provide scaffolded question prompts on the challenge card, such as step-by-step hints for setting up equations.
• At Level: Encourage independent problem solving while offering reminders about proportionality and graph interpretation.
• Above Level: Add an additional twist to the bonus question: “What happens if the supplier allows only 150 gallons at $1.50 per gallon before the rate increases?”

---

Assessment:

• Formative Assessment: Observe group collaboration and problem-solving strategies during the activity.
• Summative Assessment: Review the accuracy of calculations, graphs, and written explanations on their challenge cards.

---

Extension Activity:

• If time permits or if students finish early, pose a follow-up question:
  “How could you use equations to predict water usage for an entire month?”

---

End Note for Teachers:
This hands-on activity encourages critical thinking while connecting math concepts to real-life scenarios. It’s designed to foster collaboration, creativity, and excitement for mathematics in your classroom.